Current cellular technologies are based on the concept of coherent communication, in which the channel matrix used for demodulation is estimated via reference or pilot signals. Coherent systems, however, involve a significant increase of the signalling overhead, especially when the number of transmission points is increased or when the mobile channel changes rapidly, which motivates the use of non-coherent techniques. This letter extends the use of non-coherent communications to a multi-user (MU) multiple-input multiple-output (MIMO) framework by combining superposition coding with a reduced-complexity detection method. Numerical results confirm that our scheme achieves higher user rates than non-coherent MU transmission based on time multiplexing. In addition to the well-known sum-rate gain of MU systems, an extra performance gain given by downlink non-coherent MU communication is shown and qualitatively justified.